A Fast Simulation Approach to Switched Systems

We propose a new fast simulation approach for linear switched systems based on parareal with a model reduced coarse propagator. By using the idea of parareal and the advantage of model order reduction (MOR), we provide two strategies. One is dealing with the generalized transfer function of a whole LSS, and the other is dealing with the transfer function of each subsystem. All of them use expansions of Laguerre functions and constructions of Krylov subspaces to obtain projection matrices. The property of coefficient-matching for a kind of special switched system is proved. The Laguerre parameters for different switched subsystems can be selected by heuristic search algorithms. Further, the MOR-enhanced parareal approach for and the theoretical parallel speedup are analyzed. Finally, the effectiveness of the proposed method is illustrated by two benchmark examples.